VIce President Mike Pence and members of his family boarding Air Force Two in Dublin on Tuesday. Mr. Pence stayed at President Trump’s resort in Doonbeg, Ireland, during the official visit.CreditCreditPeter Morrison/Associated Press

House Democrats, furious over President Trump’s continued promotion of his branded properties for government business, said on Friday that they would scrutinize whether two recent cases would violate the Constitution’s ban on presidents profiting from domestic or foreign governments.

In both cases, the Democrats argued, Mr. Trump stands to benefit financially from American taxpayer dollars, and in the case of the potential summit in Doral, from foreign funds as well. The Constitution’s emoluments clauses prohibit presidents from accepting any payment from federal, state or foreign governments beyond their official salary.

“The committee does not believe that U.S. taxpayer funds should be used to personally enrich President Trump, his family, and his companies,” wrote Representative Elijah E. Cummings, Democrat of Maryland and the chairman of the Oversight and Reform Committee. The cases in question, he added, could be a conflict of interest.

In a letter of his own, Representative Jerrold Nadler, Democrat of New York and the chairman of the Judiciary Committee, raised what could be a more troubling outcome for the president. He said his committee was considering potential violations of the ban on profiting from the presidency as part of its impeachment investigation.

“Potential violations of the foreign and domestic emoluments clauses of the Constitution are of grave concern to the committee as it considers whether to recommend articles of impeachment,” he wrote. The letter was also signed by Representative Steve Cohen, Democrat of Tennessee, who leads a relevant subcommittee.

The White House did not immediately comment on the letters.

Mr. Trump and Mr. Pence drew sharp criticism this week after the vice president and his coterie of family, aides and security stayed a night at the Trump International Golf Links & Hotel in Doonbeg during a trip to Ireland, despite the fact that it was 181 miles from his meetings in Dublin. Government receipts for such stays usually run in the tens of thousands of dollars — or far more, depending on the size of the group and the length of stay.

Mr. Pence’s chief of staff initially told reporters that the vice president, who has family roots in Doonbeg, had chosen the accommodation at the “suggestion” of Mr. Trump. Facing a flurry of criticism for the choice, the vice president’s office later released a statement saying that “at no time did the president direct our office to stay at his Doonbeg resort.”

Mr. Cummings’s request asked for documents showing itemized expenses from the most recent Ireland trip, any communications related to Mr. Pence’s accommodations, and records related to Mr. Trump’s own stay at the Doonbeg resort during an official visit to Ireland in June.

“We haven’t found anything that could even come close to competing with it,” he said.

Most recently, the United States has hosted Group of 7 summit meetings at Camp David, the presidential retreat in Maryland, under former President Barack Obama, and Sea Island, Ga., under George W. Bush.

Democrats and ethics experts have criticized Mr. Trump’s use of his private properties since he took office. In addition to his own frequent visits — with an expensive coterie of aides and security in tow — most of Mr. Trump’s cabinet members and about half of House Republicans have been seen at or spent money at Trump-branded properties, according to an independent tally. And a Center for Responsive Politics count found that close to $20 million has been spent since 2015 at the Trump hotels by political groups, including those of Mr. Trump.

Mr. Trump turned over management of his company, the Trump Organization, to his oldest sons and an executive through a trust. Most presidents have used a blind trust for their finances, but Mr. Trump’s family and a close associate controls his trust. He receives updates about its business and remains the trust’s sole beneficiary.

The latest examples of the administration’s use or plans to visit his private properties have pushed the president’s critics into a frenzy.

“The Doral situation reflects perhaps the first publicly known instance in which foreign governments would be required to spend foreign government funds at President Trump’s private businesses in order to engage in official diplomatic negotiations and meetings with the United States,” Mr. Nadler and Mr. Cohen wrote.